Chalobah, 18, has largely impressed during his loan spell at Watford, and is predicted a very bright future.
In spite of his outstanding showings in the Championship this season, it is highly unlikely that he will see much playing time next term should he decide to remain at Stamford Bridge.
Arsenal plan to take advantage of the situation and snatch him away from the Blues by promising him more playing time.
The talented midfielder is aware that the Gunners would give him a much better chance of breaking into the first team set-up and might be interested in a move to the Emirates.
Chalobah, who can be used in both midfield and defence, has been exceeding expectations this season, making 26 Championship appearances for Watford and scoring 4 goals in the process.